Since its adolescence more than four decades ago, the New York Philharmonic’s home at Lincoln Center has been known as Avery Fisher Hall. Now, as the orchestra prepares for a major renovation expected to cost more than $500 million, the Fisher family has agreed to relinquish the name so the Philharmonic and Lincoln Center can lure a large donor with the promise of rechristening the building.

The unusual agreement, announced on Thursday, is a significant turnaround from 12 years ago, when the family of Avery Fisher, the music philanthropist who gave $10 million in 1973 to support the building, threatened legal action if the concert hall was rebuilt or renovated under a new name.

Lincoln Center is essentially paying the family $15 million for permission to drop the name and has included several other inducements, like a promise to feature prominent tributes to Mr. Fisher in the new lobby of the concert hall.

While the ability to raise money through naming opportunities has become a staple tool for arts organizations, perhaps no event speaks louder to its utility as a fund-raising mechanism than Lincoln Center’s willingness to pay the family of a veteran donor to step away so it can court a new benefactor.

Organizations like the Philharmonic and Lincoln Center cannot hope to raise the sums required for ambitious reconstructions or expansions without being able to dangle the carrot of a donor’s name emblazoned over the door.

“This unties the Gordian knot,” Katherine G. Farley, Lincoln Center’s chairwoman, said of the agreement. She said it was too early in the process to discuss whose name might replace Mr. Fisher’s on the building or what the price tag for such a high-profile philanthropic mantle might be.

The New York State Theater at Lincoln Center became the David H. Koch Theater in 2008, when Mr. Koch, the oil-and-gas billionaire, contributed $100 million toward its renovation. That same year, the New York Public Library’s flagship on Fifth Avenue at 42nd Street was named for Stephen A. Schwarzman, a Wall Street financier who donated $100 million toward that building’s expansion.

The Fisher agreement, which came together over the last three months, was made with the three children of Mr. Fisher, who died in 1994: Nancy Fisher, Charles Avery Fisher and Barbara Fisher Snow.

“We’re very pleased that it happened in such a pleasant and quick manner,” Charles Fisher said.

Jed Bernstein, Lincoln Center’s president, said he ran into Nancy Fisher at a dinner party in June and invited her and other family members to his office for discussions. The tone of the negotiations was considerably more amicable than it had been the last time around, the Fishers said. “It was us and them,” Nancy said. “It’s not like that anymore.”

In addition, the renovation of the rest of Lincoln Center, completed two years ago, made the Fishers realize how much the hall needed to be refreshed; it was the only major building that was not part of the campus transformation, designed by Diller Scofidio & Renfro. The acoustics have long been considered problematic, and the audience amenities sorely need updating.

“I watched as the campus started to change,” Nancy Fisher said. “It invited the public in, it didn’t look so forbidding and formal anymore.” She added that the new energy generated by the renovated spaces at Lincoln Center had pointed up Avery Fisher Hall’s mustiness.

“The hall was like an old slipper,” she said. “How could you avoid sensing that?”

In 1973, Mr. Fisher, founder of the Fisher electronics company, donated $10.5 million toward the renovation of the former Philharmonic Hall, erected in 1962, which was then renamed for him. The pledge agreement setting forth the conditions of his gift included the stipulation that Avery Fisher Hall “will appear on tickets, brochures, program announcements and advertisements and the like, and I consent in perpetuity to such use.”

Some more recent agreements have sunset provisions, like Mr. Koch’s with the State Theater, which says the building can be renamed for a new donor after 50 years, with members of the Koch family retaining the right of first refusal.

Lincoln Center sweetened its deal with the Fisher family in several ways. Mr. Fisher will be inducted into a new Lincoln Center Hall of Fame in the renovated building, which will celebrate artists, leaders and philanthropists who have played central roles at Lincoln Center. Their contributions will be explored in interactive installations that highlight all 11 of Lincoln Center’s constituent organizations.

A Fisher family member will serve on the Hall of Fame’s advisory board and on the selection committee for inductees into its Avery Fisher Classical Music Wing, which will contain archival materials about Mr. Fisher.

The agreement also promises to give a higher profile to the Avery Fisher Artist Program, established in 1974, which awards prizes to established American instrumentalists of distinction and career grants to emerging young artists.

In addition, a Philharmonic concert conducted by the orchestra’s music director, Alan Gilbert, that honors Avery Fisher and his family has been scheduled for March 24.

The $15 million that Lincoln Center will pay the family will come from a line of credit that will ultimately be covered by the gift of the new donor. The family said it had not determined how that money would be distributed.

The Philharmonic is planning a comprehensive interior reconstruction, to begin in 2019, that will retain the building’s exterior, designed by Max Abramovitz.

Gary Parr, the orchestra’s chairman, said the renaming opportunity would enable the project to be an ambitious undertaking. “We’re not going to do something minor or small,” he said. “Being able to do this makes a huge difference in the prospects of raising the funds to be successful.”

While the renovation is underway, the goal is to limit the Philharmonic’s time outside the hall to two seasons, during which the orchestra will play in various New York City locations that have not been determined so far.

An architect for the new hall has yet to be selected. Although the Philharmonic board voted in 2005 to proceed with a design by the British architect Norman Foster, the thinking has evolved since then, and the orchestra is starting over. Akustiks has been chosen as the acoustics firm and Fisher Dachs Associates as the theater designer.

“This is in sight now; it’s really happening,” Mr. Bernstein said. “Donors want to be assured of the likelihood of these projects.”

The Fisher family didn’t come to this decision easily; every member was involved: all three children, their spouses and five grandchildren.

For Lincoln Center, the issue may have been one of financial reality as it faced the daunting budget of a major renovation. For the family, the issues were more personal.

“Would this have made him proud?” Nancy Fisher’s son, Philip Avery Kirschner, 34, said of his grandfather. “What were his original intentions?”

Ultimately, the family determined that the most important thing was to make possible the continuing presentation and excitement of classical music at Lincoln Center, just as Mr. Fisher had in the first place.

“His goal was to give back to music lovers what they had given him,” Charles Fisher said. “We feel, at the end of the day, that our father would have wanted this as well.”

Correction:

An earlier version of a graphic that appeared with this article misstated the former name of a section of the Metropolitan Opera. It was the Alberto W. Vilar Grand Tier, not Pier.

A version of this article appears in print on , on Page A1 of the New York edition with the headline: Goodbye, Avery Fisher. Hello, Somebody Else.. Order Reprints | Today’s Paper | Subscribe